Let me answer my own question. Not really an answer to fix the problem but I found the problem and somehow could at least get back on Lion. I tried almost everything that I could think but none worked to get Mavericks on it.
The issue is Mavericks and Mountain Lion both somehow not detecting my Intel SSD.
I connected this mac in Target disk mode and could see it there. Ran DU checks and no issues reported. I then tried Mavericks installation from USB disk and then too it didn't find this disk.
I then formatted this disk from another mac (In Target) disk mode and started internet recovery. This time internet recovery started for Mountain Lion and that too couldn't detect this SSD same like Mavericks Internet Recovery as well.
Then I decided to go back to Lion and see if Lion installed/recovery detects this work and to my surprise Lion recovery detected it. So clearly some compatibility issue. I had no Lion installer on USB or elsewhere so I decided to install Lion on it from my another Mac's recovery.
I started it again in Target disk mode and connected it to another mac running Lion that I started into recovery. From there I could see this disk via firewire and then I installed Lion on it. After first reboot in between the installation I was worried if the installer continues on the same firewire "Macintosh HD" or goes into self "Macintosh HD" but it was proper.
Finally I rebooted both Macs with their own respective HDs as startup disks and both booted fine.
I still wonder what is wrong with my SSD that works for Lion but not for Mountain Lion or Mavericks. Not sure if it's SSDs fault or these latest OSes have dropped support for some SSDs or something like that.